function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta


sigmoid_res = sigmoid( (theta' * X')' );
J = sum(sum( (-y .* log( sigmoid_res )) - (1-y) .* log( 1 - sigmoid_res ) ) / length( y )) + sum( theta .^ 2 ) * lambda / (2*length(y));
                      
J -= (theta(1) ^ 2) * lambda / (2 * length(y));
                      
grad = (sigmoid_res - y)' * X / length( y ) + theta' .* lambda / m;
grad(1) -= theta(1) * lambda / m;

% =============================================================

end
